The present invention addresses the issue of peak-limited data channels. While many conventional coding schemes suggest the superposition of many channels which are separated in the frequency domain, they all assume that the superposition will not pose serious problems such as overloading the channel. When the number of superposed channels is relatively small, this concern may indeed not arise in most applications. Several conventional systems contemplate superposing many hundreds if not thousands of signals per channel. Channel overloading may therefore become a serious problem.
Furthermore, the present invention addresses the overloading issue for a particular method of signal superposition, the Fourier transform method, which is becoming more commonly used in the field. See U.S. Pat. No. 4,679,227 to Hughes-Hartogs (the '227 patent), for example. The '227 patent teaches a modem which uses 256 channels superposed together. However, the '227 patent ignores the peak limited (e.g., overloading) problem. Based on the fact that traditional signaling such as QAM avoid overloading altogether, the problem is generally ignored even in the theory community. Fourier Transform Coding (FTC) sections data into contiguous blocks, codes in the Frequency Domain, computes the Discrete Fourier Transform (DFT) of the code, and then transmits a continuous signal whose sampled values at the Nyquist rate are the output of DFT. See Weinstein et al., "Data Transmission by Frequency-Division Multiplexing Using the Discrete Fourier Transform," IEEE Trans. on Comm. Tech. Vol. COM-19, No. 5, Oct. 1971. Practical methods of FTC coding and decoding are also discussed by Feig et al., "Sequence Transmission: Coding in the Frequency Domain," Presented at the Advanced International Workshop on Sequences Honoring Paul Erzos' 75the Birthday, Pasitano, Italy, Jun. 1988, (also appeared in Sequences, I.M. Capocelli, ed., Springer-Verlag, 1990).
A reduced computational method and adaptive equalization for FTC coding are introduced by Peled et al. in their article titled, "Frequency Domain Data Transmission Using Reduced Computational Complexity Algorithms,"
Proc. IEEE Intl. Conf. on coustics, Speech, and Signal Processing, Denver Colo. pp. 964-967, Apr. 1980. See "Linear Methods for High-Density Magnetic Recording of Data" by Ephraim Feig, IEEE Transactions on Magnetics, Vol. 25, No. 3, 1989, for a discussion of how to endure errors due to clipping at peak amplitude values.
FTC processed signals sometimes have very large amplitude segments which must be clipped at some prescribed peak value .+-. P in order to retain channel linearity, because peak-limited channels can not accept arbitrarily large impulses. (See Feig et al., "The Performance of Fourier Transform Division Multiplexing Schemes on Peak Limited Channels," IBM RC 1988; Feig et al., "Digital Implementation of Frequency Division Multiplexing on Peak-Limited Channels," IBM RC 14440, Feb. 1989; and Ephraim Feig, "Fourier Transform Coding for Peak Limited Channels," Proc. of the Twenty Sixth Annual Allerton Conf. on Communicaton, Control, and Computing, 1988.) In conventional systems the clipped sequence rather that the original DFT output is passed through a lowpass filter and then the data is transmitted. This technique clearly ignores the information corresponding to the clipped signal. A need therefore exists to convey both the clipped signal and the error over peak limited channels.